Batalin-Tyutin quantization of the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">CP</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn><mn></mn></mrow></msup></mrow></math></span> model

N. Banerjee; Subir Ghosh; R. Banerjee

doi:10.1103/PhysRevD.49.1996

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Batalin-Tyutin quantization of the ${CP}^{N - 1}$ model

N. Banerjee^*

Subir Ghosh

R. Banerjee

Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Calcutta 700064, India

Gobardanga Hindu college, North 24-Parganas, West Bengal, India

S. N. Bose National Center for Basic Sciences, Sector I, DB 17, Salt Lake, Calcutta-700064, India

^*Electronic address: shila@saha.ernet.in

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Phys. Rev. D 49, 1996 – Published 15 February, 1994

DOI: https://doi.org/10.1103/PhysRevD.49.1996

Abstract

The ${CP}^{N - 1}$ model is quantized in the generalized canonical formalism of Batalin and Tyutin by converting the original second-class system to first class. Operator-ordering ambiguities present in the conventional quantization scheme of Dirac are thereby avoided. The first-class constraints, the involutive Hamiltonian, and the BRST charge are explicitly computed. The partition function is defined and evaluated in the unitary gauge.

References (16)

P. A. M. Dirac, Lectures on Quantum Mechanics (Yeshiva University Press, New York, 1964)
M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, NJ, 1992)
I. A. Batalin and E. S. Fradkin, Nucl. Phys. B279, 514 (1987) Phys. Lett. B 180, 157 (1986)
I. A. Batalin and I. V. Tyutin, Int. J. Mod. Phys. A 6, 3255 (1991)
E. Gozzi and A. Guha, J. Math. Phys. 24, 1213 (1983)
P. Mitra and R. Rajaraman, Ann. Phys. (N.Y.) 203, 137 (1990)
A. Kovner and B. Rosenstein, Phys. Rev. Lett. 59, 857 (1987)
N. Banerjee, Subir Ghosh, and R. Banerjee, Nucl. Phys. B (to be published)
M. Moshe and Y. Oz, Phys. Lett. B 224, 145 (1989) P. P. Srivastava, ibid. 235, 287 (1990)
T. Fujiwara, Y. Igarashi, and J. Kubo, Nucl. Phys. B341, 695 (1990) Y. Kim, S. Kim, W. Kim, Y. Park, K. Kim, and Y. Kim, Phys. Rev. D 46, 4574 (1992)
R. Banerjee, H. J. Rothe, and K. D. Rothe, "Batalin-Fradkin quantisation of anomalous chiral gauge theories," Heidelberg Report No. 1993/35, 1993 (unpublished)
J. Kowalski-Glikman, Phys. Lett. B 245, 79 (1990) S. Ghosh, Phys. Rev. D (to be published)
I. A. Batalin and I. V. Tyutin, Mod. Phys. Lett. A 7, 1931 (1992)
R. Banerjee, H. J. Rothe, and K. D. Rothe, "Batalin-Fradkin quantisation of the unitary gauge Abelian Higgs model," Heidelberg Report No. 1993/36, 1993 (unpublished)
E. S. Fradkin and G. A. Vilkovisky, Phys. Lett. 55B, 224 (1975)
M. Henneaux, Phys. Rep. 126, 1 (1985) M. HenneauxClassical Foundations of BRST Symmetry (Bibliopolis, Naples, 1988)

[c1] P. A. M. Dirac, Lectures on Quantum Mechanics (Yeshiva University Press, New York, 1964)

[c2] M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, NJ, 1992)

[c3] I. A. Batalin and E. S. Fradkin, Nucl. Phys. B279, 514 (1987) Phys. Lett. B 180, 157 (1986)

[c4] I. A. Batalin and I. V. Tyutin, Int. J. Mod. Phys. A 6, 3255 (1991)

[c5] E. Gozzi and A. Guha, J. Math. Phys. 24, 1213 (1983)

[c6] P. Mitra and R. Rajaraman, Ann. Phys. (N.Y.) 203, 137 (1990)

[c7] A. Kovner and B. Rosenstein, Phys. Rev. Lett. 59, 857 (1987)

[c8] N. Banerjee, Subir Ghosh, and R. Banerjee, Nucl. Phys. B (to be published)

[c9] M. Moshe and Y. Oz, Phys. Lett. B 224, 145 (1989) P. P. Srivastava, ibid. 235, 287 (1990)

[c10] T. Fujiwara, Y. Igarashi, and J. Kubo, Nucl. Phys. B341, 695 (1990) Y. Kim, S. Kim, W. Kim, Y. Park, K. Kim, and Y. Kim, Phys. Rev. D 46, 4574 (1992)

[c11] R. Banerjee, H. J. Rothe, and K. D. Rothe, "Batalin-Fradkin quantisation of anomalous chiral gauge theories," Heidelberg Report No. 1993/35, 1993 (unpublished)

[c12] J. Kowalski-Glikman, Phys. Lett. B 245, 79 (1990) S. Ghosh, Phys. Rev. D (to be published)

[c13] I. A. Batalin and I. V. Tyutin, Mod. Phys. Lett. A 7, 1931 (1992)

[c14] R. Banerjee, H. J. Rothe, and K. D. Rothe, "Batalin-Fradkin quantisation of the unitary gauge Abelian Higgs model," Heidelberg Report No. 1993/36, 1993 (unpublished)

[c15] E. S. Fradkin and G. A. Vilkovisky, Phys. Lett. 55B, 224 (1975)

[c16] M. Henneaux, Phys. Rep. 126, 1 (1985) M. HenneauxClassical Foundations of BRST Symmetry (Bibliopolis, Naples, 1988)

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Batalin-Tyutin quantization of the ${CP}^{N - 1}$ model

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Batalin-Tyutin quantization of the ${CP}^{N - 1}$ model